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“Schwinger model” on the fuzzy sphere. (English) Zbl 1208.81191

Summary: We construct a model of spinor fields interacting with specific gauge fields on the fuzzy sphere and analyze the chiral symmetry of this ”Schwinger model”. In constructing the theory of gauge fields interacting with spinors on the fuzzy sphere, we take the approach that the Dirac operator \(D_{q}\) on the \(q\)-deformed fuzzy sphere \(S^2_{qF}\) is the gauged Dirac operator on the fuzzy sphere. This introduces interaction between spinors and specific one-parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators \(D_{q}\) and \(D\) alone. Using the path integral method, we have calculated the \(2n\)-point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T13 Yang-Mills and other gauge theories in quantum field theory
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations

References:

[1] DOI: 10.1088/0264-9381/9/1/008 · Zbl 0742.53039 · doi:10.1088/0264-9381/9/1/008
[2] DOI: 10.1142/9789812707468 · doi:10.1142/9789812707468
[3] Chu C-S., JHEP 0108 pp 038–
[4] Steinacker H., JHEP 0503 pp 075–
[5] O’Connor D., JHEP 0708 pp 066–
[6] DOI: 10.1142/S0217751X01003482 · Zbl 0986.81108 · doi:10.1142/S0217751X01003482
[7] DOI: 10.1016/S0370-2693(01)00641-4 · Zbl 0969.81594 · doi:10.1016/S0370-2693(01)00641-4
[8] Vaidya S., JHEP 0201 pp 011–
[9] DOI: 10.1016/S0550-3213(02)00028-7 · Zbl 0985.81058 · doi:10.1016/S0550-3213(02)00028-7
[10] DOI: 10.1016/S0550-3213(03)00048-8 · Zbl 1009.81035 · doi:10.1016/S0550-3213(03)00048-8
[11] DOI: 10.1007/s002200050011 · Zbl 0954.58026 · doi:10.1007/s002200050011
[12] Balachandran A. P., Int. J. Mod. Phys. A 16 pp 17–
[13] DOI: 10.1063/1.533271 · Zbl 0979.81083 · doi:10.1063/1.533271
[14] DOI: 10.1142/S0217732308025656 · doi:10.1142/S0217732308025656
[15] Martin X., JHEP 0404 pp 077–
[16] Panero M., JHEP 0705 pp 082–
[17] Landi G., An Introduction to Noncommutative Spaces and Their Geometries (1997) · Zbl 0909.46060
[18] DOI: 10.1007/BF00739805 · Zbl 0840.58011 · doi:10.1007/BF00739805
[19] DOI: 10.1007/BF02099460 · Zbl 0920.58007 · doi:10.1007/BF02099460
[20] DOI: 10.1007/BF02099720 · Zbl 0872.58008 · doi:10.1007/BF02099720
[21] DOI: 10.1007/BF02506411 · Zbl 0873.58005 · doi:10.1007/BF02506411
[22] DOI: 10.1142/S0217751X9800161X · Zbl 0959.58005 · doi:10.1142/S0217751X9800161X
[23] DOI: 10.1142/S0217732300001389 · doi:10.1142/S0217732300001389
[24] DOI: 10.1023/A:1007518622795 · Zbl 0957.81090 · doi:10.1023/A:1007518622795
[25] DOI: 10.1016/S0393-0440(01)00070-5 · Zbl 1046.54002 · doi:10.1016/S0393-0440(01)00070-5
[26] DOI: 10.4310/ATMP.2008.v12.n3.a5 · Zbl 1149.81020 · doi:10.4310/ATMP.2008.v12.n3.a5
[27] Saemann C., JHEP 0802 pp 111–
[28] Dolan B. P., JHEP 0803 pp 029–
[29] Paschke M., Acta Phys. Pol. B 31 pp 1897–
[30] Varilly J. C., Commun. Math. Phys. 221 pp 511–
[31] DOI: 10.1016/S0370-2693(01)00670-0 · Zbl 0969.81532 · doi:10.1016/S0370-2693(01)00670-0
[32] DOI: 10.1007/s00220-005-1383-9 · Zbl 1090.58504 · doi:10.1007/s00220-005-1383-9
[33] Harikumar E., JHEP 0609 pp 037–
[34] DOI: 10.1088/1751-8113/40/13/023 · Zbl 1114.81028 · doi:10.1088/1751-8113/40/13/023
[35] DOI: 10.1016/S0393-0440(00)00068-1 · Zbl 1130.81346 · doi:10.1016/S0393-0440(00)00068-1
[36] DOI: 10.1016/S0393-0440(02)00023-2 · Zbl 1130.81347 · doi:10.1016/S0393-0440(02)00023-2
[37] Klimcik C., Commun. Math. Phys. 199 pp 257–
[38] DOI: 10.1007/s002200000213 · Zbl 0955.58004 · doi:10.1007/s002200000213
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